The Polyhedral Geometry of Truthful Auctions

Joswig, Michael; Klimm, Max; Spitz, Sylvain

doi:10.1007/978-3-031-32726-1_17

Lecture Notes in Computer Science

2023

DOI: 10.1007/978-3-031-32726-1_17

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The Polyhedral Geometry of Truthful Auctions

Michael Joswig

Max Klimm

Sylvain Spitz

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2024

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The polyhedral geometry of truthful auctions

Joswig,

Klimm,

Spitz

2024

Math. Program.

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The difference set of an outcome in an auction is the set of types that the auction mechanism maps to the outcome. We give a complete characterization of the geometry of the difference sets that can appear for a dominant strategy incentive compatible multi-unit auction showing that they correspond to regular subdivisions of the unit cube. Similarly, we describe the geometry for affine maximizers for n players and m items, showing that they correspond to regular subdivisions of the m-fold product of $$(n-1)$$ ( n - 1 ) -dimensional simplices. These observations are then used to construct mechanisms that are robust in the sense that the sets of items allocated to the players change only slightly when the players’ reported types are changed slightly.

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The polyhedral geometry of truthful auctions

Joswig,

Klimm,

Spitz

2024

Math. Program.

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The Polyhedral Geometry of Truthful Auctions

Cited by 1 publication

References 38 publications

The polyhedral geometry of truthful auctions

The polyhedral geometry of truthful auctions

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